SOLUTION: Find all solutions to the equation 9sin(x)=8−sin(x) in the interval 0≤x≤2π. If there is more than one answer, enter your answers as a comma separated list.

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions to the equation 9sin(x)=8−sin(x) in the interval 0≤x≤2π. If there is more than one answer, enter your answers as a comma separated list.       Log On


   

Question 995823: Find all solutions to the equation 9sin(x)=8−sin(x) in the interval 0≤x≤2π. If there is more than one answer, enter your answers as a comma separated list.
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Found 2 solutions by ikleyn, stanbon:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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9sin(x) = 8 - sin(x).

9sin(x) + sin(x) = 8,

10sin(x) = 8,

sin(x) = 8%2F10 = 4%2F5.

x = arcsin(4/5).                     This angle is in the 1-st quadrant.

x = pi - arcsin(4/5).             This angle is in the 2-nd quadrant.

There are no other solutions in this interval/segment [0, 2pi].


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions to the equation 9sin(x)=8−sin(x) in the interval 0≤x≤2π. If there is more than one answer, enter your answers as a comma separated list.
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10*sin(x) = 8
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sin(x) = 0.8
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x = arcsin(0.8) = 53.13 degrees or x = 180-53.13 = 126.87 degrees
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Cheers,
Stan H.
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